To tell the truth, I don't remember the chapter on particle motion in college physics clearly. In my impression, the equation of motion is a displacement-time equation, and the trajectory equation does not contain time.

If I remember correctly, the equation of motion is a parametric equation, taking the plane coordinate system as an example:

x=f(t)

y=g(t)

After removing the time parameter t from the above equation:

x=F(y)

It's the trajectory equation

Maybe it's a little different. It's better to look at college physics-mechanics. After all, I learned it six years ago, but it has been useless for a long time and I almost forgot.